1206.5119 (F. G. Scholtz et al.)

Spectral triplets, statistical mechanics and emergent geometry in
non-commutative quantum mechanics    [PDF]

F. G. Scholtz, B. Chakraborty

We show that when non-commutative quantum mechanics is formulated on the Hilbert space of Hilbert-Schmidt operators (referred to as quantum Hilbert space) acting on a classical configuration space, spectral triplets as introduced by Connes in the context of non-commutative geometry arise naturally. A distance function as defined by Connes can therefore also be introduced. We proceed to give a simple and general algorithm to compute this function. Using this we compute the distance between pure and mixed states on quantum Hilbert space and demonstrate a tantalizing link between statistics and geometry.

View original: http://arxiv.org/abs/1206.5119